Theorems · Theorem · field theory
Complex.ofReal_pow
∀ (r : ℝ) (n : ℕ), ↑(r ^ n) = ↑r ^ n
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 81 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Complex.ofRealstatement and proof · cited by 1,654
- pow_zeroproof · cited by 1,094
- pow_succproof · cited by 374
- Complex.ofReal_mulproof · cited by 180
Cited by81
Results whose statement or proof uses this declaration.
- Orientation.oangle_selfproof · cited by 17
- Real.sin_sq_add_cos_sqproof · cited by 12
- Real.exp_nat_mulproof · cited by 6
- HurwitzZeta.evenKernel_defproof · cited by 6
- Real.inv_one_add_tan_sqproof · cited by 4
- norm_cexp_neg_mul_sqproof · cited by 4
- Real.cos_two_mulproof · cited by 4
- Real.cosh_sqproof · cited by 3
- ProbabilityTheory.complexMGF_id_gaussianRealproof · cited by 3
- hasSum_mellin_pi_mul_sqproof · cited by 3
- Complex.meromorphicOrderAt_canonicalFactorproof · cited by 3
- Real.cos_sqproof · cited by 3